Find the sine, cosine, and tangent of each angle using the unit circle.
$\theta=225\degree,\left(-\frac{\sqrt2}{2},-\frac{\sqrt2}{2}\right)$

• A. $\sin\theta=-\frac{\sqrt2}{2},\cos\theta=-\frac{\sqrt2}{2},\tan\theta=2$
• B. $\sin\theta=\frac{\sqrt2}{2},\cos\theta=-\frac{\sqrt2}{2},\tan\theta=-1$
• C. $\sin\theta=-\frac{\sqrt2}{2},\cos\theta=-\frac{\sqrt2}{2},\tan\theta=1$
• D. $\sin\theta=\frac{\sqrt2}{2},\cos\theta=\frac{\sqrt2}{2},\tan\theta=\frac{\sqrt2}{1}$

Answer: (C)

Verified step by step guidance

1. The unit circle is a circle with a radius of 1 centered at the origin of the coordinate plane. Each point on the unit circle corresponds to an angle θ measured from the positive x-axis.
2. For an angle θ = 225°, we are in the third quadrant of the unit circle. In this quadrant, both sine and cosine values are negative.
3. The coordinates of the point on the unit circle corresponding to θ = 225° are given as (-√2/2, -√2/2). These coordinates represent (cosθ, sinθ).
4. Therefore, for θ = 225°, we have cosθ = -√2/2 and sinθ = -√2/2.
5. The tangent of an angle θ is given by tanθ = sinθ/cosθ. Substituting the values, we get tanθ = (-√2/2) / (-√2/2) = 1.